Problem: Solve for $x$ and $y$ using substitution. ${-5x+5y = 5}$ ${y = 4x+7}$
Solution: Since $y$ has already been solved for, substitute $4x+7$ for $y$ in the first equation. ${-5x + 5}{(4x+7)}{= 5}$ Simplify and solve for $x$ $-5x+20x + 35 = 5$ $15x+35 = 5$ $15x+35{-35} = 5{-35}$ $15x = -30$ $\dfrac{15x}{{15}} = \dfrac{-30}{{15}}$ ${x = -2}$ Now that you know ${x = -2}$ , plug it back into $\thinspace {y = 4x+7}\thinspace$ to find $y$ ${y = 4}{(-2)}{ + 7}$ $y = -8 + 7$ $y = -1$ You can also plug ${x = -2}$ into $\thinspace {-5x+5y = 5}\thinspace$ and get the same answer for $y$ : ${-5}{(-2)}{ + 5y = 5}$ ${y = -1}$